Abstract
This study intends to demonstrate the value of using the partial order set theory comparing different but intertwined sets of indicators or indexes. We illustrate this approach by analysing the relative positions (partial order) of a set of countries with consideration for environmental and development indicators. Using data from 2013, the analysis mainly covers the countries with economies having a strong impact on climate change—China, the USA, the European Union (member States), India, Russian Federation, Japan, Brazil, Canada, and Mexico. The concepts of total and partial orders, linear extension or comparability are introduced and used in the analysis. The inclusion of three integrative environmental indicators and two development indicators (human development index and GDP per capita) shows that in 2013 the BRICS were the worst positioned countries. In contrast, several countries in Northern Europe (Denmark, followed by Germany, Ireland, the Netherlands, Sweden and the UK) were associated with the best overall indicators. Canada is not comparable to any other country, the values of its indicators being sometimes higher and sometimes lower than those associated to any other country considered in this study. The USA, comparable to a single country, shows a similar behaviour for the same reasons.
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Notes
- 1.
In Hammond et al. (1995), p. 1.
- 2.
See http://www.un.org/geninfo/bp/enviro.html (accessed 20 July, 2018).
- 3.
In Meadows (1998), pp. 4–5.
- 4.
Meadows (1998), p. 12.
- 5.
Conscious Uncoupling? Low Carbon Economy Index, 2015. www.pwc.co.uk/sustainability, accessed 20 July, 2018.
- 6.
The international diffusion of SDGs, anticipated in recent years, probably catalyses efforts—particularly national ones—in this rapidly evolving field of research.
- 7.
Consider, for example, the various products providing information on environmental variables but derived on the basis of data obtained from the same sensors on board satellites and corrected according to the same standardized procedures (and themselves based on models with a limited accuracy).
- 8.
See http://www.investopedia.com/ask/answers/199.asp (accessed 20 July, 2018).
- 9.
http://data.worldbank.org/indicator/NY.GDP.MKTP.CD (accessed 20 July, 2018).
- 10.
On the development of such matrix, see Hammond et al. (1995), pp. 13–16.
- 11.
Say in 2016, the Yale Center for Environmental Law & Policy and Yale Data-Driven Environmental Solutions Group at Yale University, the Center for International Earth Science Information Network at Columbia University, in collaboration with the Samuel Family Foundation, McCall MacBain Foundation, and the World Economic Forum.
- 12.
See https://epi.envirocenter.yale.edu/2018-epi-report/methodology (accessed 20 July, 2018).
- 13.
Such as the conservation of biodiversity, the sustainable management of marine and ocean resources or health issues in their human, animal and ecosystem dimensions.
- 14.
https://treaties.un.org. Accessed 20 July, 2018.
- 15.
Note that when A < B holds, we can say in a general way that A is smaller than B.
- 16.
Let us emphasize that an “empty order” is not a set with no elements, but simply that its elements are not comparable in pairs.
- 17.
The maximum height of an order with 36 countries is 35, which would correspond to a total order.
- 18.
Our use of the term “country group” does not coincide with a class gathering a set of incomparable countries.
- 19.
To know the countries “higher” (resp. “lower”) than a country X and their number, just follow on the graph all the paths starting from that country X following the direction (resp. the inverse direction) of the oriented links, list and count the labels of the vertices encountered.
- 20.
This need does not exist a priori in the comparative analysis of country performances.
- 21.
In accordance with certain basic assumptions, this impossibility has been demonstrated mathematically by K. Arrow in 1951, see Saari (2001).
- 22.
One can also build scenarios to assess the impact of the improvement of a country index values.
- 23.
In particular many products are derived from intensive processing of data supplied by sensors on board satellites, and are used to monitor multi-scales environmental changes (land use and land cover, sea level, atmospheric composition, etc.).
- 24.
Note that the simple aggregation of indices, producing a total order, reduces even more sharply—crushes somehow—the analysis space.
- 25.
As long as they are not weighted in the aggregation process as it is the case in CCPI (see Sect. 12.2).
- 26.
hdr.undp.org/en/content/income-gini-coefficient. Accessed on September 19, 2016. The top ten countries in the GINI rank were in 2013: Norway, Australia, Switzerland, Netherlands, USA, Germany, New Zealand, Canada, Singapore and Denmark.
- 27.
He found that inequality tended to decrease with robust economic growth in the 1950s. Then he had a lot of criticism afterwards because he did not consider public policy choices in his economic analysis.
- 28.
According to the World Bank Development Report 2014: “more than 20 percent of the population in developing countries live on less than $1.25 a day, more than 50 percent on less than $2.50 a day and nearly 75 percent on $4 a day”.
- 29.
See the Sustainable Development Knowledge Platform at https://sustainabledevelopment.un.org/ (accessed 20 July, 2018).
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Acknowledgements
This study is a contribution (PM and CL) to the GEMA project “Gouvernance Environnementale: Modélisation et Analyse” funded by CNRS (Défi interdisciplinaire: «InFIniti» InterFaces Interdisciplinaires Numérique et Théorique).
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Mazzega, P., Lajaunie, C., Leblet, J., Barros-Platiau, A.F., Chansardon, C. (2019). How to Compare Bundles of National Environmental and Development Indexes?. In: Boulet, R., Lajaunie, C., Mazzega, P. (eds) Law, Public Policies and Complex Systems: Networks in Action. Law, Governance and Technology Series, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-11506-7_12
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